Band gap optimization of one-dimension elastic waveguides using spatial Fourier plane wave expansion coefficients

Author(s)

Lima, Vinicius D. ^[1] ; Villani, Luis G. G. ^{[1, 2]} ; Camino, Juan F. ^[1] ; Arruda, Jose R. F. ^[1]

Affiliation

^[1] Univ Campinas UNICAMP, Sch Mech Engn, Campinas, SP - Brazil

^[2] Fed Univ Espirito Santo UFES, Dept Mech Engn, Av Fernando Ferrari 514, BR-29075910 Vitoria, ES - Brazil

• Document type: Journal article
• Source: PROCEEDINGS OF THE INSTITUTION OF MECHANICAL ENGINEERS PART C-JOURNAL OF ME; v. 235, n. 14, SI JAN 2021.
• Web of Science Citations: 0

Abstract

Periodic elastic waveguides, such as rods, beams, and shafts, exhibit frequency bands where wave reflections at impedance discontinuities cause strong wave attenuation by Bragg scattering. Such frequency bands are known as stop bands or band gaps. This work presents a shape optimization technique for one-dimensional periodic structures. The proposed approach, which aims to maximize the width of the first band gap, uses as tuning parameters the spatial Fourier coefficients that describe the shape of the cell cross-section variation along its length. Since the optimization problem is formulated in terms of Fourier coefficients, it can be directly applied to the Plane Wave Expansion (PWE) method, commonly used to obtain the dispersion diagrams, which indicate the presence of band gaps. The proposed technique is used to optimize the shape of a straight bar with both solid and hollow circular cross-sections. First, the optimization is performed using the elementary rod, the Euler-Bernoulli and Timoshenko beam, and the shaft theoretical models in an independent way. Then, the optimization is conducted to obtain a complete band gap in the dispersion diagrams, which includes the three wave types, i.e., longitudinal, bending, and torsional. All numerical results provided feasible shapes that generate wide stop bands in the dispersion diagrams. The proposed technique can be extended to two- and three-dimensional periodic frame structures, and can also be adapted for different classes of cost functions. (AU)

• FAPESP's process: 18/15894-0 - Periodic structure design and optimization for enhanced vibroacoustic performance: ENVIBRO
• Grantee: Carlos de Marqui Junior
• Support Opportunities: Research Projects - Thematic Grants
• FAPESP's process: 20/07703-0 - Dynamics of quasi-periodic elastic structures
• Grantee: Luis Gustavo Giacon Villani
• Support Opportunities: Scholarships in Brazil - Post-Doctoral